2 citations · 3 across the 11 of their papers we have counts for
13 papers
A Group Analogue of the Ghurye--Olkin--Ibragimov Theorem
Gennadiy Feldman
According to the classical Skitovich--Darmois theorem, the Gaussian distribution on the real line is characterized by the independence of two linear forms of a finite number of ind…
An Analogue of Heyde's Theorem for Discrete Torsion Abelian Groups with Cyclic -Components
Gennadiy Feldman
According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of ind…
Heyde characterization theorem for some classes of locally compact Abelian groups
Gennadiy Feldman
Let and be linear forms of real-valued independent random variables. By Heyde's theorem, if the conditional distribution of given is symmetric, then the ran…
An Analogue of Heyde's Theorem for a Certain Class of Compact Totally Disconnected Abelian Groups and p-quasicyclic Groups
Gennadiy Feldman
According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of indepen…
Characterization of probability distributions on some locally compact Abelian groups containing an element of order 2
Gennadiy Feldman
The well-known Heyde theorem characterizes the Gaussian distributions on the real line by the symmetry of the conditional distribution of one linear form of independent random vari…
Heyde theorem for locally compact Abelian groups containing no subgroups topologically isomorphic to the 2-dimensional torus
Gennadiy Feldman
We prove the following group analogue of the well-known Heyde theorem on a characterization of the Gaussian distribution on the real line. Let be a second countable locally com…
On the Li--Zheng theorem
Gennadiy Feldman
By the well-known I.Kotlarski lemma, if , , and are independent real-valued random variables with nonvanishing characteristic functions, and $L_2=ξ_2-…
Arithmetic of a certain semigroup of probability distributions on the group
Gennadiy Feldman
We consider a certain convolution semigroup of probability distributions on the group , where is the group of real numbers and $\ma…
On a characterization of shifts of Haar distributions on compact open subgroups of a compact Abelian group
Gennadiy Feldman
Let X be a compact Abelian group. In the article we obtain a characterization of shifts of Haar distributions on compact open subgroups of the group X by the symmetry of the condit…
On analogues of C.R.Rao's theorems for locally compact Abelian groups
G. M. Feldman
Let , , be independent random variables with nonvanishing characteristic functions, and , be real numbers such that for . Le…
Independent random variables on Abelian groups with independent the sum and difference
G. M. Feldman
Let X be a second countable locally compact Abelian group. Let be independent random variables with values in the group X and distributions such that the sum…
On a functional equation appearing in characterization of distributions by the optimality of an estimate
G. Feldman, P. Graczyk
Let be a second countable locally compact Abelian group containing no subgroup topologically isomorphic to the circle group . Let be a probability distribution…
Independent linear statistics on the cylinders
G. M. Feldman, M. V. Myronyuk
Let either or $X=Σ_\text{\boldmath $a$}\times\mathbf{T}$, where is the additive group of real number, is the cycle group an…